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Long-Time Behaviour in a Model of Microtubule Growth

Part of: Equilibrium statistical mechanics Special processes

Published online by Cambridge University Press:  01 July 2016

O. Hryniv  and
M. Menshikov
O. Hryniv*
Affiliation:
Durham University
M. Menshikov*
Affiliation:
Durham University
*
∗ Postal address: Department of Mathematical Sciences, Durham University, Science Laboratories, South Road, Durham DH1 3LE, UK.
∗ Postal address: Department of Mathematical Sciences, Durham University, Science Laboratories, South Road, Durham DH1 3LE, UK.
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Abstract

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We study a continuous-time stochastic process on strings made of two types of particle, whose dynamics mimic the behaviour of microtubules in a living cell; namely, the strings evolve via a competition between (local) growth/shrinking as well as (global) hydrolysis processes. We give a complete characterization of the phase diagram of the model, and derive several criteria of the transient and recurrent regimes for the underlying stochastic process.

Keywords

Microtubuletransiencerecurrencephase transitionbirth-and-death process

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 82B41: Random walks, random surfaces, lattice animals, etc.
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 42 , Issue 1 , March 2010 , pp. 268 - 291
Copyright
Copyright © Applied Probability Trust 2010 

References

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